New Delhi: The University Grants Commission (UGC) has proposed a draft mathematics curriculum for undergraduates, featuring ancient Indian concepts like sutra-based arithmetic and algebra, ‘kala ganana’ (time calculation), ‘Bharatiya innovations’, and geometry from the shulva sutras of the Vedic period.
The Council has invited stakeholder feedback on the draft curriculum, which is aligned with the Learning Outcomes-based Curriculum Framework (LOCF) under the National Education Policy (NEP) 2020.
The LOCF emphasises on clearly defined skills and knowledge students should gain by the completion of the course. Under the LOCF , courses are categorised into Major, Minor, Skill, and Value-Added Courses (VAC).
In a notification issued 20 August, UGC Secretary Manish Joshi said the draft will serve as a model curriculum to encourage flexibility and innovation in programme design and syllabus development.
The draft curriculum for mathematics focuses on various ancient Indian concepts. It proposes to teach sutra-based algebra (ancient Indian method using mathematical formulas) as a minor or additional course under the undergraduate programmes.
Under this, the UGC has recommended teaching the history and development of Bharatiya Bijaganita (Indian algebra), division of polynomials using the Paravartya Yojayet Sutra (a traditional Vedic Mathematics technique meaning ‘transpose and apply’).
The UGC has also proposed a course on Kala Gaṇana (traditional Indian timekeeping), exploring how ancient Indian scholars calculated time using the Sun, Moon, stars, and the Earth’s motion.
The proposed curriculum dives into texts like the Sūrya Siddhānta and Āryabhaṭīyam, explains the structure of cosmic time—from Yugas and Kalpas to Brahma’s day (Brahma Varṣa)—and introduces divine time cycles like Vishnu Varṣa and Shiva Varṣa. Students will learn about the panchaṅga (Indian calendar) and how it determines auspicious moments (muhūrtas) used in rituals and festivals.
It also covers ancient observatories, the prime meridian of Ujjain, and how ancient Indian Vedic time units of Ghatis and Vighatis compare with modern systems like Greenwich Mean Time (GMT) and Indian Standard Time (IST).
The course blends astronomy, mythology, and culture—bringing India’s rich time-science heritage to life.
Professor Amber Habib, Department of Mathematics at the Shiv Nadar University, raised concerns over the dominance of ancient Indian content in the curriculum.
It is quite possible, he argued, that a graduate of this course will have expertise in what was happening in Indian mathematics till about the 15th century, but their knowledge of modern mathematics will be essentially confined to that of the early 20th century.
“A graduate of this curriculum is in no way prepared for modern research and will find it difficult to cope even with the Master’s programmes of national institutions like IITs and IISERs (Indian Institutes of Science Education and Research),” he said.
Philosophy of Indian mathematics
The draft curriculum proposes a value-added course on 12th-century Indian mathematician and astronomer Bhaskara II and his book Līlāvatī, a poetic Sanskrit text on arithmetic and geometry.
Outlining the course objectives, the UGC proposal states, “To understand the Lilavati methods for basic operations on integers and rational numbers. To understand the formulae for various sums of natural numbers in arithmetic and geometric progressions.”
The UGC also proposed another course on the philosophy of Indian mathematics. The course introduces Bhāratīya philosophical systems, explores the role of mathematics in personality development, and offers a brief study of the Vedas, Vedāṅgas, Purāṇas, and Darśanas.
It also covers Bhāratīya Bījagaṇit (Indian algebra) and the use of mathematics in Arthaśāstra and Chhandaśāstra.
“After completing the course, the learner will be able to understand Bhāratīya philosophical texts such as the Vedas, Darśanas, and Purāṇas, and gain insights into the role of mathematics in ancient disciplines like Arthaśāstra, Chhandaśāstra (prosody), as well as its application in personality development,” the draft stated.
‘Bharatiya innovations’
The UGC draft curriculum proposes a course on ‘Bharatiya Innovations’, widely accepted and acknowledged. Its main objectives are to introduce the Bharatiya perspective of mathematics, highlight key contributions in arithmetic, algebra, geometry, and trigonometry.
It also seeks to understand how this knowledge spread globally and examine why this rich history has often been overlooked or erased.
Under this course, the UGC has proposed topics including the sum of squares and cubes of terms in arithmetic progression, the nth-order sum of natural numbers and terms in Mahavira’s Chitichitika and Adhikahinagunasankalitam.
The course also explores the interactions between ancient Bharat and Greece, the transmission of mathematics and calculus to Arab and European countries, and investigates why this significant history was often ignored or erased. Additionally, it covers the influence of Bharatiya concepts on computer science and cryptography, as well as their impact on modern mathematical research and traditions.
The draft curriculum also proposes a value-added course on mathematics in the Narada Purana.
This course aims to introduce the significance of the Puranas in Bharatiya tradition, focus on the mathematical concepts and techniques related to basic arithmetic operations and geometry found in the Narada Purana, explore their applications in daily life, and develop problem-solving skills using the mathematical tools and methods described in the text.
(Edited by Ajeet Tiwari)
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